The survey, by pollsters Find Out Now, put Nigel Farage’s party in second place behind the Tories, with Labour third.
It suggests British politics is now a three-way fight between the Conservatives, Reform UK and Labour, with the parties separated by just three points.
The Tories are on 26%, one point down on Find Out Now’s last poll a week ago.
Reform UK are up two points to 24%, leapfrogging Labour, who have dropped two points to 23%.
The Lib Dems are way behind on 11%, with the Greens on 9% and the SNP on 3%.
According to the Electoral Calculus website, the same result at the next general election would lead to political chaos.
The Conservatives would be the biggest party on 219, well short of the 326 seats needed for a Commons majority.
Labour would be eight seats behind on 207 seats, with Reform UK on 95, the Lib Dems on 67, the SNP on 22 and the Greens on six.
Even a Tory/Reform UK coalition would still fail to command a majority, as would a rainbow pact involving Labour, the Liberal Democrats, the SNP and Greens.
The findings are a blow for Keir Starmer, who unveiled Labour’s “plan for change” today as he tries to get the government back on the front foot following five months of difficult headlines.
Among his promises was a pledge to bring down legal and illegal immigration - a key demand of Reform UK voters - because it is “what working people want”.